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8

Let me first answer your actual question (and then I'll proceed to answer something slightly different that I think will be informative and helpful). Your question asks whether it's possible to use only a DSA key. Technically speaking, this is of course possible. The reason is that a DSA key has exactly the same format as an ElGamal key. No one forces you to ...

2

Sure you can do. There are many lattice attacks, using your second assumption, to ECDSA (which also applied to DSA). For instance see Smart and Howgrave-Graham and Shparlinski and Nguyen. All the lattice attacks base on finding small solutions (for the ephemeral key $k$ and the private key $a$) to the signing equation $sk-ra\equiv H(m)\pmod q.$ If you have ...

2

ECDH is not for signing. Your sign method using ecdh does not look like any valid signature scheme I have ever seen, and is therefore likely wildly insecure. Note that the Q&A you link to is asking a very different question.

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